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Lesson Study as a form of in-School
Professional Development:
Case studies in two post-primary schools
Aoibhinn Ní Shúilleabháin School of Mathematical Sciences University College Dublin
January 2015
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Lesson Study as a Model of in-school Professional Development
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ContentsAcknowledgements .................................................................................................................... 3
Abbreviations ............................................................................................................................. 4
Introduction ................................................................................................................................ 5
Educational Reform and Professional Development ................................................................. 6
Teacher Community ................................................................................................................... 6
Teacher Learning and Lesson Study ...................................................................................... 7
Pedagogical Content Knowledge ............................................................................................... 9
Methodology ............................................................................................................................ 11
Participating Case-study Schools ......................................................................................... 11
Findings.................................................................................................................................... 15
Lesson Study Cycle .............................................................................................................. 15
Stage 1: Formulate/Reflect on Goals & Study Curriculum ............................................. 15
Stage 2: Plan a selected or revised research lesson .......................................................... 16
Stage 3: Conduct/Observe research lesson ...................................................................... 19
Stage 4: Reflect on the research lesson ............................................................................ 22
Teacher Learning ................................................................................................................. 24
Developing Pedagogical Content Knowledge ................................................................. 24
Changes to Classroom Practices ...................................................................................... 29
In-School Professional Development .................................................................................. 31
Complementing In-service Workshops............................................................................ 31
School Management ......................................................................................................... 31
Voluntary Professional Development .............................................................................. 31
Scalability ........................................................................................................................ 32
Sharing Resources ............................................................................................................ 32
Limitations of the Research ................................................................................................. 33
Conclusion ............................................................................................................................... 34
References ................................................................................................................................ 35
Appendices ............................................................................................................................... 39
Appendix A: The Lesson Study Cycle ................................................................................. 39
Appendix B: Materials for use during lesson study ............................................................. 46
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Figures
Figure 1 Lesson study cycle adapted from Lewis et al. (2009) ................................................. 7 Figure 2 Framework of Mathematical Knowledge for Teaching from Ball et al. (2008) ....... 10 Figure 3 Resources utilised during planning meetings ............................................................ 14 Figure 4 Brain-storm for over-arching goal ............................................................................. 16 Figure 5 Planning a series of lessons ....................................................................................... 18 Figure 6 Mind-mapping lesson plan ........................................................................................ 19 Figure 7 Sample teacher observation sheet .............................................................................. 21 Figure 8 Sample of student work utilised for reflection .......................................................... 22 Figure 9 Contextualised question designed by teachers .......................................................... 27 Figure 10 Contextualised student-inquiry activity ................................................................... 28 Figure 11 Suggested headings for a Teaching & Learning plan .............................................. 42
Tables
Table 1 Lesson study cycle and meeting times……………………………………………..13
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Acknowledgements
This research would not have been possible without the generosity of the Mathematics
teachers who gave so freely of their time, expertise, and knowledge throughout this study.
Furthermore the principals, staff, and students of the two schools involved were incredibly
important in welcoming this educational research to their schools and in supporting their
colleagues participating in the project.
This report is based in part on my doctoral dissertation completed at the School of Education,
Trinity College Dublin, under the supervision of Dr. Aidan Seery. The research reported here
was assisted by the National Council of Curriculum and Assessment who supported the two
post-primary schools participating in this research. This study was also sponsored by an
Ussher Fellowship postgraduate award from Trinity College Dublin.
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Abbreviations
KCS Knowledge of Content and Students
KCT Knowledge of Content and Teaching
NCCA National Council for Curriculum and Assessment
PCK Pedagogical Content Knowledge
PMDT Project Maths Development Team
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Introduction
This research investigated the introduction of a model of in-school professional development
which would support mathematics teachers in their practices at a time of curriculum reform.
Lesson study, a model of Japanese origin, was a model that would provide teachers with a
structure within which they could collaborate and engage with new pedagogical practices
encouraged as part of the Project Maths initiative. Twelve teachers in two post-primary
schools volunteered to participate in the research which lasted for one academic year.
Qualitative data was generated in both schools through audio recordings of all teacher
meetings conducted around lesson study and through interviews with participating teachers.
The researcher participated in the investigation as a participant-observer in facilitating the
introduction of lesson study to teachers and in participating in meetings as a former
Mathematics teacher. The data was analysed thematically in iterative stages utilising a
framework of pedagogical content knowledge (PCK) as suggested by Ball, Thames, and
Phelps (2008).
Data analysis suggests that as a result of teachers’ participation in lesson study, teachers
developed their PCK and incorporated reform teaching approaches as part of their classroom
practices. A number of teachers reported that their familiarity with and confidence in teaching
the new mathematics syllabus improved. Furthermore, teacher communities of both schools
developed through their participation in lesson study. Findings related to teacher learning and
to the introduction of lesson study in two Irish post-primary schools are reported here.
This report is written as a summary of findings on research into teacher professional
development which was supported by the NCCA and also as an introductory guide for
teachers interested in lesson study. All references to participating teachers and schools are
pseudonyms and any identifiable references have been removed from this report.
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Educational Reform and Professional Development
Teachers play a key role in educational reform. Reforms typically impose new demands on
the already complex work of teaching and it is therefore important that teachers are provided
with professional development supports and opportunities to engage meaningfully with any
reforms they are being asked to implement (Charalambos & Philippou, 2010; Hanley &
Torrance, 2011; Remillard & Bryans, 2004).
This research was conducted following the introduction of Project Maths. This revised
syllabus brought with it a change in content taught to post-primary mathematics students and
also encouraged a change in the approach to the teaching and learning of mathematics from a
commonly traditional exposition-based classroom (Lyons, Lynch, Close, Sheerin, & Boland,
2003; Oldham, 2001), to one encouraging communication of mathematical thinking with a
focus on developing students’ higher-order problem-solving skills. While structured in-
service professional development opportunities were offered to teachers as part of this
particular curriculum reform, this research investigated an alternative model of supporting
teachers in their practices through school-based teacher community.
Teacher Community
A challenge in achieving sustainable reform is that most teachers teach alone in isolated
classrooms without the opportunity to observe other teachers or reflect on their own practices
(Remillard, 2005). While there is much recent focus on the social elements of learning for
students, research increasingly refers to the importance of considering the social dimensions
of learning for teachers (Grossman, Wineburg, & Woolworth, 2001; Hord, 2004) and it is
widely recognised that teacher communities figure among the most important factors for
promoting educational change within schools (de Lima, 2001; OECD, 2009). A key rationale
for teacher community is that it provides an ongoing venue for teacher learning, provides
teachers with social structures for professional collaboration and collegiality, and provides
teachers with a means to engage with educational and curricular policies within the
environment and realities of their own schools (Darling-Hammond, Chung Wei, Andree,
Richardson, & Orphanos, 2009; Dooner, Mandzuk, & Clifton, 2008; Guskey, 2002; Louis &
Marks, 1998; T. H. McLaughlin, 2004; M. W. McLaughlin & Talbert, 2006; van den Akker,
2003).
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Teacher Learning and Lesson Study
Lesson study is a form of teacher professional development that is based on teacher
collaboration and teacher community. The expression ‘lesson study’ is a literal translation
from the Japanese word Jugyokenky where jugyo means lesson and kenkyu refers to study or
research. The translation can be misleading in a sense that lesson study is more than a study
of lessons, but rather is an investigation of teachers into their own practices through planning,
conducting, observing, and reflecting on research lessons (Conway & Sloane, 2005; C.
Fernandez, Cannon, & Chokshi, 2003; Corcoran, 2011a; Fernández & Robinson, 2006;
Murata, Bofferding, Pothen, Taylor, & Wischnia, 2012; Murata & Takahashi, 2002;
Takahashi & Yoshida, 2004).
A cycle of lesson study consists of the following steps portrayed in Figure 1:
Figure 1 Lesson study cycle adapted from Lewis et al. (2009)
As part of the first step, teachers decide on an overall goal for their teaching which will guide
their practices in lesson study. Teachers then directly access the curriculum, decide on a topic
to teach within that cycle, and build a lesson plan around particular learning objectives
(Lewis, Perry, & Hurd, 2009). Following step 2 of collaboratively planning content and
materials for the lesson, one teacher conducts the research lesson while other members of the
lesson study community attend and observe that lesson. This observation of the research
1. Formulate/Reflect on Goals &
Study Curriculum
2. Plan a selected or revised research
lesson
3. Conduct/Observe research lesson
4. Reflect on the research lesson using data generated within
the lesson
(4a. Revise the research lesson)
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lesson is an important phase of the cycle which differs to other forms of teacher observation
since all teachers have engaged with the planning and observation of the lesson. Teachers
then collectively reflect on the lesson and may decide to alter and re-teach it or continue to
another cycle of lesson study (Fernandez & Chokshi, 2004).
Since this investigation occurred during a time of reform of the post-primary mathematics
curriculum, it was important to incorporate professional development practices which would
support teachers in engaging with the reform and in encouraging changes to traditional
classroom practices. Remillard (2000) and Hanley & Torrance (2011) note that through
engaging directly with curriculum materials and through seeing a curriculum enacted,
teachers are encouraged to incorporate changes to their practices as part of curriculum
reform. The four stages of lesson study directly reflect these curriculum reform practices of
engaging with and enacting curriculum materials. Furthermore, lesson study encompasses
observation and reflection which encourages teachers to notice student mathematical thinking
during research lessons and structures teachers’ reflection on their own pedagogical practices
(Corcoran, 2011b; Jacobs, Lamb, & Philipp, 2010; Mason, 2002; van Es & Sherin, 2008).
Previous research conducted both in Ireland and internationally suggests that participation in
lesson study holds potential to develop teachers’ content and pedagogical content knowledge
(Corcoran, 2011b; C. Fernandez et al., 2003; Leavy, Hourigan, & McMahon, 2010; Lewis,
Perry, & Murata, 2006). Murata et al. (2012) found that primary teachers developed in their
understanding of student learning through conversations around planning a research lesson.
Aligning with Murata et al.’s (2012) research, Cjakler et al. (2013), in their study involving
four UK secondary school mathematics teachers, found that teachers began to develop less
teacher-centred approaches and focused more on students’ thinking through participating in
lesson study. In Lewis et al.’s (2009) research they concluded that teacher participation in
lesson study impacted on their teaching and learning practices and beliefs and Dudley (2013)
found that teachers were more inclined to build in new approaches or take ‘risks’ in their
teaching due to participation in lesson study. These studies suggest that through participation
in lesson study, teachers are provided with opportunity to build on their understanding of
teaching and learning approaches, to begin to incorporate new practices in their own
teaching, and to develop in their approach to building students’ mathematical understanding.
Furthermore as a form of professional development, participation in lesson study can help
teachers develop a sense of community so that introduction of reforms can feel less daunting
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and more manageable as a consequence of developing of collaborative pedagogy (Lewis et
al., 2009).
Leading from this rich research literature, this study aimed to investigate whether lesson
study could be introduced as a form of professional development within Irish post-primary
mathematics departments. In addition the research questioned how participation in lesson
study would impact on teachers’ PCK, referencing new pedagogical approaches highlighted
within the Project Maths initiative.
Pedagogical Content Knowledge
Mathematics education research has found that while teachers’ subject content knowledge
can be an important factor in teaching mathematics (Campbell et al., 2014; Hill, Rowan, &
Ball, 2005; Krauss et al., 2008), teachers’ PCK also plays a vital role in students’ learning
experiences (Deborah L. Ball, Thames, & Phelps, 2008; Campbell et al., 2014; Hill, Ball, &
Schilling, 2008). Shulman (1976) first referenced ‘pedagogical content knowledge’ as the
knowledge unique to teachers as an amalgam of content and pedagogy which allows teachers
to represent information in a number of ways that are particular and relevant to their own
students. While there are a number of frameworks of mathematical knowledge for teaching
(Rowland, 2014), in this research the multi-dimensional nature of teacher knowledge is
incorporated within a framework suggested by Ball et al. (2008) which encompasses
teachers’ knowledge of mathematics and how to teach that mathematics to their students
(Figure 2).
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Figure 2 Framework of Mathematical Knowledge for Teaching from Ball et al. (2008)
Focusing on PCK as constructed by Ball et al. (2008), knowledge of content and students
(KCS) refers to teachers’ understanding of how students learn particular content and includes
teachers’ knowledge of common misconceptions students have. Knowledge of content and
teaching (KCT) combines teachers’ knowledge of various approaches and strategies which
can be utilised in teaching a particular topic and the various questions which might best
illuminate a topic for students. These elements of PCK will be further explored as findings in
this research.
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Methodology
This investigation was conducted as a double case study in two post-primary schools, Doone
and Crannóg, which were involved in separate phases of the national curriculum roll-out.
Twelve mathematics teachers volunteered to participate in the research and teachers taught
students in all year-groups at all levels of assessment.
Qualitative data was generated in this research through audio recordings of all teacher
meetings around lesson study and through individual teacher interviews held at separate
stages during the research. Supplementary artefacts such as teacher notes, lesson plans, field
notes, samples of student work, and a researcher log formed part of the structuring of data
analysis, but were not considered as sources of data within the study. Teachers had autonomy
in deciding when and how often they met as a lesson study community and had full
independence in deciding the curriculum content to be taught in their research lessons.
The researcher engaged with the teachers in both schools as a participant-observer in
facilitating initial phases of lesson study in participating in lesson study as a former
mathematics teacher in a phase 1 school and in interviewing participating teachers using
semi-structured interview guides. In order to minimise bias, analysis did not commence until
all of the data had been generated. Audio files were transcribed and analysis of the data was
carried out in four phases guided by a general analytic strategy as suggested by Braun and
Clarke (2006). New themes and codes identified as part of the analysis were related to the
literature on lesson study and teacher learning and were incorporated within a framework of
mathematical knowledge for teaching as suggested by Ball et al. (2008)1.
Participating Case-study Schools
Doone is a boy’s school of approximately 550 students. Five of the nine mathematics
teachers chose to participate in the research and all but one of the teachers taught more than
one subject. Crannóg has a mixed gender cohort of approximately 800 students. Seven of the
ten mathematics teachers at the school chose to participate in this research and of these, five
teachers taught mathematics as the only subject in their time-table. These two schools had
participated in different phases of the Project Maths curriculum roll-out.
1 Further detailing of the methodology and analysis can be referenced in the doctoral thesis that is the basis for this report (Ni Shuilleabhain, 2014a)
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The lesson study groups participating in both schools included teachers of varying
experiences ranging from over thirty years teaching experience to newly qualified teachers.
Both schools were urban based as a necessity of this research project. Referencing Ríordáin
& Hannigan’s (2011) study stating that approximately one half of teachers teaching
mathematics at post-primary level are unqualified to do so, two of the twelve teachers were
recognised as ‘out-of-field’.
As discussed in their initial lesson study meetings, teachers in both schools had a number of
reasons to volunteer to participate in the research ranging from feeling unsure and
unconfident in teaching the revised syllabus, to wanting to investigate new ways in which
they could collaborate as a Mathematics department.
Teachers had authority over when they would meet as a lesson study community, what the
content of research lessons would be, what students would be taught, and how many lesson
study cycles they would complete during the academic year. Research lessons were therefore
developed for both a mix of junior and senior students and over a range of mathematical
topics from investigation of quadratic patterns to introducing Pythagoras’ Theorem. Teacher
meetings were held, on average, once every two weeks and each meeting lasted on average
one hour (see Table 1).
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Table 1 Lesson study cycles and meeting times
School Crannóg Doone
Lesson Study
Cycle
Lesson Content Duration
(Hr:Mins)
Lesson Content Duration
(Hr:Mins)
1
Introducing quadratic
patterns
0:36
1:19
1:44
1:08
1:23
1:03 (p-l)
Introducing the
concept of x-
squared
0:44
0:41
1:49
0:35
1:55
1:19 (p-l)
2
Factorising quadratic
expressions utilising
concrete resources
0:57
1:27
1:01
0:47 (p-l)
Multiplying
Fractions:
Developing a sense
of measure
1:13
1:27
1:16
1:04
0:31 (p-l)
3
Factorising quadratic
expressions utilising
concrete resources (2)
1:01 (p-l)
Exploring quadratic
expressions through
application
1:13
1:16
0:30
0:23 (p-l)
4
Differentiation in
Calculus: Applications
1:18
1:16
1:57
0:29 (p-l)
0:43
Introducing
Pythagoras’
Theorem
1:07
0:45
0:38
1:29
0:13 (p-l)
* p-l = post-lesson discussion
Teachers utilised, but were not restricted to, lesson study guidelines for the collaborative
planning of research lessons (Appendix A) and to record the lesson plan (Appendix B)
adapted from Lewis et al. (2011). During planning meetings resources such as syllabuses,
research literature, teacher magazines, teaching and learning plans, and textbooks were
utilised (Figure 3). Meetings took place in various classrooms or common teacher areas in the
schools and were held during the school day at times where the majority of teachers were
free, with a small number of meetings held after school.
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Figure 3 Resources utilised during planning meetings
In the following section lesson study processes, notable findings and items for consideration
from the research are detailed.
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Findings
A number of findings and contributions are reported here, further details of which may be
found in additional research literature (Ni Shuilleabhain, 2014a, 2014b). These are
categorised in this report as:
Lesson study cycle,
Teacher learning, and
School-based professional development
Lesson Study Cycle
For the purposes of this report, findings of teachers’ engagement in lesson study will initially
be reviewed through a framework of the lesson study cycle. It is envisaged that this
framework should provide the reader with greater insight into lesson study as a model of
school based professional development and teacher community.
Stage1:Formulate/ReflectonGoals&StudyCurriculum
As their overall goal for lesson study, teachers in both Doone and Crannóg identified
students’ engagement with and attitudes towards mathematics as important classroom issues
to address. Following a discussion around their pedagogical experiences, teachers in Doone
highlighted that the majority of their students did not identify with mathematics as a
meaningful subject and wanted to incorporate these affective issues within their teaching of
research lessons during the year. Their overall goal was summarised as the following:
For our students to find purpose and meaning in their mathematics that leads to their enjoyment and confidence in the subject.
In Crannóg’s first lesson study meeting, teachers noted that students were often reticent in
engaging in the subject and their participation in class was often prohibited by their fear of
giving an incorrect answer. After brain-storming a number of ideas within the meeting
(Figure 4), teachers agreed on the following over-arching goal:
To endeavour to create a culture which fosters independent thinking and fearlessness, leading to autonomous learning.
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These overall goals provided teachers with a philosophical basis for structuring their research
lessons and, at the end of the research, teachers reported in their individual interviews that
they felt these aims had been achieved through the various lesson study cycles.
Figure 4 Brain-storm for over-arching goal
In deciding on strands of Mathematics on which to focus, teachers chose areas of the subject
which they felt least confident in teaching or identified topics which they felt could be further
developed for student understanding (see Table 1). As can be concluded from Table 1, the
majority of research lessons were planned either for junior cycle or transition year classes.
Due to the nature of the final state assessments, teachers did not wish to interrupt teaching of
third year or senior cycle students as research lessons but this is not to suggest that research
lessons could not also be conducted within these year groups.
Stage2: Planaselectedorrevisedresearchlesson
In beginning the planning of lessons teachers originally referenced the lesson study
guidelines given to them at the beginning of the research (Appendix A). This provided
teachers with a structure through which they could collaborate with one another in deciding
on the content and sequencing of activities within a research lesson. Following the initial two
cycles, teachers became familiar with the processes of planning within their communities and
no longer referenced the guidelines for direction.
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A sample lesson template provided in the guidelines (Appendix B) was originally utilised by
teachers to record their research lesson, but by the final cycles in both schools teachers had
adapted these and used their own format to record the details of their research lessons.
In planning the research lessons, it was important that any work involved occurred during the
meetings and that teachers did not undertake independent work outside of school. Teachers
found that work undertaken outside of meetings often led to incoherence in the research
lesson and therefore any activities, worksheets, or questions that were to be incorporated
within a research lesson were developed during the meetings.
Materials were designed in a variety of ways during planning meetings utilising research
literature, teacher magazines, on-line resources, or textbooks incorporating new and
innovative ideas. In Doone, teachers developed contextualised activities through breaking
into teams of two or three and devising questions to be incorporated within the lesson.
Teachers then shared these questions, attempted these activities in order to anticipate
students’ thinking, and positively critiqued one another’s work ensuring that the language,
symbols, and numbers incorporated within problems were relevant to particular groups of
students. Where teachers externally sourced activities these were shared with their colleagues
during meetings and were modified as relevant, contextualised tasks for students. In Crannóg
teachers often collectively built on one another’s ideas in designing and incorporating new
ideas within research lessons. Developing ideas from research literature such as articles from
teacher magazines or books on mathematics education also added to the incorporation of new
and innovative ideas within research lessons in both schools.
As a surprising outcome of this research, instead of planning one research lesson in isolation
teachers in both schools began independently developing series of lessons within which a
research lesson was included. This provided teachers with a better understanding of how
students’ mathematical thinking could be developed within a topic and highlighted the prior
knowledge necessary for students to meet the learning objective within the research lesson
(Figure 5). In their final meeting in Crannóg Eileen, an early career teacher, commented that
planning a series of lessons was one of the most useful outcomes of lesson study:
Eileen For each of them we always managed to come up with a series of lessons, we never just planned one lesson – we always had at least a week or six classes.
Fiona So even though you’re looking at a lesson as the focus of it –
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Eileen There was always an intro[duction] into it and the afterwards was planned as well.
Dave We had a topic planned as well as a lesson planned.
Eileen You do get more out of that than just one lesson plan. You’re getting a section.
Figure 5 Planning a series of lessons
In Doone’s final research cycle teachers mind-mapped their series of lessons and found this
format beneficial in ordering their thinking (Figure 6).
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Figure 6 Mind-mapping lesson plan
In Michael’s final interview, he extolled the virtues of planning and explained how he felt
this stage of the lesson study cycle had benefitted the group.
Michael I’m not going to say I like planning but it’s useful…It’s been a very positive experience for me. I’ve enjoyed it and I’ve got a lot out of it so it’s been good. It really shows me that planning is not only important but that it’s productive as well and it’s a very useful thing to do… It’s just working in teams, working with the people that you work with, there’s just so many potential benefits in it.
Collaborative planning provided teachers with opportunities to share their teaching
experiences with one another but also to build their awareness of different mathematical
strategies and develop their focus on students’ mathematical thinking.
Stage3:Conduct/Observeresearchlesson
While the conducting teacher may, at times, have been nervous about teaching in front of
their colleagues, all teachers reflected on this stage of the lesson study cycle as a very
positive learning experience. While it was an unusual for teachers to invite colleagues into
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their classroom to observe a lesson, the collective nature of planning led to a supportive
environment for those conducting the lesson as expressed by Kate in her mid-point interview:
Kate So we were saying this actually ourselves, we were saying it’s not that I’m not even nervous about it - I’ll probably be a bit nervous the day I have to do it - but we planned the lesson, it’s our lesson, so it’s kind of like we’re teaching it as well… I found that with Owen for instance – I was laughing at things he was saying [in the lesson]. He’s just himself in the class, so is Lisa. But I wasn’t really looking at them, I was more looking at what they were teaching and how it was said and how the kids were picking up…It was like we’ve all planned it so if it fails it’s all of our faults.
Not all teachers were free to observe each research lesson, but it was important that a
majority of the group observed and reflected on how students engaged with the research
lesson.
In observing the research lessons teachers found it most beneficial to track one pair or one
group of students for the duration of the lesson in order to better notice and interpret how
student thinking developed and how students responded throughout the lesson.
In their individual interviews teachers reported that they found observing students for the
duration of a lesson to be incredibly beneficial to their practice, providing them with insight
on students’ thinking which encouraged teachers to reflect on their own individual classroom
practices.
Gerald It’s great to be able to sit there and watch that group working. They were engaged and you could follow the train of thought and give them time because you are not under pressure to run off to another group. If you are a single teacher you can’t follow the train of thought around all the groups and if you are delving in and giving assistance it is quite a hard thing to do that effectively.
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Teachers originally utilised observation guides based on Lewis and Hurd’s (2011) ‘Lesson
Study Step by Step: How Teacher Learning Communities Improve Instruction’ but then
developed their own observation template constructed around recording observations of
students’ thinking and students’ activities (Appendix B). It was not necessary for teachers to
maintain their observation
records but these notes
provided discussion points
for teachers in the post-
lesson discussion (Figure 7).
Teachers were initially wary
of the impact of classroom
observation on students’
learning but reflected, in
their post-lesson discussions,
that the presence of a
number of teachers within
the classroom did not have
an adverse effect on
students’ learning. Aside
from some senior students
quietly questioning why
there were so many people in
the room, teachers noted that
students seemed surprisingly unperturbed by the
larger teacher presence within the classroom.
Furthermore, observing how students communicated mathematics with one another during
small group and whole class presentations provided teachers with insight into the value of
such an approach in the teaching and learning of mathematics and into the features of
successfully facilitating class work based around communication of mathematical thinking.
As a point of interest, in observing students during a research lesson teachers found it
difficult not to intervene or engage with students while they were ‘observing’. At the end of
the research a number of teachers reflected that they would learn more from their
Figure 7 Sample teacher observation sheet
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observations if they did not engage with students in this manner and resolved to maintain
their distance as an observer in future research lessons as is recommended by the literature on
lesson study.
Stage4:Reflectontheresearchlesson
Lewis & Hurd (2011) advise that post-lesson discussions be held at as close a time following
the research lesson as is possible. In this research each of the post-lesson discussions was
held on the same day as the research lessons where teachers could reference their notes and
accurately reflect on students’ engagement, the development of the topic, the orchestration of
the lesson, and many other elements within the lesson.
In post-lesson discussions teachers often referred to their observation notes but also
referenced student work in interpreting how students engaged in activities and in assessing
whether the lesson had met its learning objective (Figure 8).
Figure 8 Sample of student work utilised for reflection
Where in their first post-lesson discussions teachers may have been wary of criticising any of
the teaching approaches, as the meetings continued teachers’ reflections focused more and
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more on students’ learning and less on the teachers’ actions. This reflection of students’
thinking led to teachers anticipating more of students’ mathematical responses and to seeing a
lesson ‘from the eyes of a student’ in subsequent planning meetings. This changing
perspective was an important element of teacher learning where members of the lesson study
community began to develop or further hone their critical student lens (Fernandez et al.,
2003) in noticing and interpreting students’ mathematical thinking (Corcoran, 2011b; Jacobs
et al., 2010). It is also worthy to note here that early career teachers who conducted research
lessons welcomed feedback on their practice from their more experienced colleagues.
These post-lesson discussions proved to be important stages of lesson study where teachers
were provided with opportunity to reflect on what they had observed in terms of interpreting
students’ strategies, recollecting student conversations, seeing the lesson through the eyes of
a student, and developing their knowledge of sequencing learning trajectories for particular
mathematical content.
Re‐teachingaresearchlesson
In cycle 2 in Crannóg, teachers decided that their lesson on factorising quadratics had not
achieved their intended learning objective and they concluded that they had included too
much content in one research lesson. Teachers reviewed their lesson plan and a different
teacher conducted the revised research lesson with a class within the same year group. In all
other cycles in both schools teachers were satisfied that the lessons had met their objectives
but re-teaching a research lesson remains a viable possibility for further developing research
lessons.
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Lesson Study as a Model of in-school Professional Development
24
KCSIdentifying prior
knowledge
Anticipating students'
mathematical thinking
Interpreting and reflecting on students'
mathematical responses
Teacher Learning
In this section a number of findings around teacher learning and around the wider school
context will be discussed.
At the end of the research all teachers reported in their final interviews that they felt they had
benefited, albeit in different ways, from participating in the research. All teachers felt they
had an improved understanding of facilitating student group work, of holding whole class
discussions, and of incorporating more communication within their mathematics classrooms.
All but one teacher felt they had an improved knowledge of and understanding of the
curriculum through engaging with curriculum documents throughout the planning of research
lessons, that one teacher having felt that they already had a deep understanding of the
curriculum prior to engaging in the research. A small number of teachers also felt their
subject matter knowledge had improved.
The following section details findings of teacher learning in terms of PCK.
DevelopingPedagogicalContentKnowledge
KnowledgeofContentandStudents
A key finding of this research is the development of teachers’ pedagogical content knowledge
through their participation in iterative cycles of lesson study. Utilising a framework of
mathematical knowledge for teaching (Ball et al., 2008), the following features of KCS
emerged as developing through teachers’ continued
planning and reflection of research lessons:
Identifying students’ prior knowledge
Anticipating students’ mathematical thinking
Interpreting and reflecting on students’
mathematical responses
Identifyingstudents’priorknowledge
What students learn in the classroom depends, to a
large extent, on what they already know (Ball &
Hyman, 2003; Holten & Thomas, 2001) and in
mathematics students can be challenged by drawing
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Lesson Study as a Model of in-school Professional Development
25
on their prior knowledge and building on the assumptions they have already made (Baumert
et al., 2010). Composing a lesson from the view point of a student and identifying their prior
knowledge forms an important part of teachers’ KCS and within the collective planning of
the research lessons, it became more and more relevant to teachers to identify the prior
knowledge that was required of students for a particular topic and to incorporate this within
the lesson. This was an important exercise since discussions around this issue provided
teachers with a definitive starting point from which to build students’ mathematical thinking
in particular topics.
Anticipatingstudents’mathematicalthinking
Through their classroom experiences teachers build on their knowledge of how students are
likely to understand or have difficulties with a topic (Schoenfeld, 2011). An experienced
teacher will know what issues are likely to be problematic and what misconceptions are
common to students (Ball et al., 2008; Krauss et al., 2008). In this research through their
observation and reflection of research lessons, teachers became more aware of anticipating
and articulating students’ mathematical thinking within subsequent research lessons and in
their own teaching.
Interpretingandreflectingonstudents’mathematicalresponses
When students construct their own mathematical understanding, there are important learning
moments for teachers to interpret and gain insight into students’ thinking. Lesson study
provides teachers with unique opportunities to observe students’ activities within a co-
constructed lesson and teachers can therefore notice, interpret and reflect on students’
learning (Breen, McCluskey, Meehan, O'Donovan, & O'Shea, 2014; Jacobs et al., 2010;
Mason, 2002). As part of participating in iterative cycles of lesson study teachers became
more aware of and began explicitly reflecting on students’ strategies and conversations
around mathematical activities during their post-lesson discussions. This benefitted teachers
in structuring subsequent research lessons and in further identifying student thinking in their
own construction and conduction of classes outside of lesson study.
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Lesson Study as a Model of in-school Professional Development
26
KnowledgeofContentandTeaching
Utilising the same framework of mathematical knowledge for teaching (Deborah L. Ball et
al., 2008), the following features of KCT emerged as developing through teachers’ continued
planning and reflection of research lessons:
Sequencing learning trajectories
Developing contextualised questions
Analysing mathematical activities
Sequencinglearningtrajectories
Sequencing material for instruction requires teachers to make connections between the
mathematics being taught and how the student can be best introduced to that topic. In order to
make these connections the teacher has to be aware of the relative demands that different
topics and tasks make of students (Rowland, 2007). In this research sequencing a learning
trajectory over a series of lessons became a fundamental matter of planning for both lesson
study communities engaged in this research and as their final output of each lesson study
cycle, teachers had detailed series of lessons through which students’ mathematical thinking
would be developed.
Developingcontextualisedquestions
In planning research lessons, teachers realised
that traditional textbook questions did not
always meet the learning objectives of the
research lesson. Teachers wanted to design
problems and activities that would be both
relevant and contextualised for students
(Schoenfeld, 1992) and developing these
activities became a common element within the
lesson study cycles in both schools. Teachers
often sourced ideas from textbooks, PMDT
curriculum materials, or education literature
supplied to them by the facilitator and then
modified these questions to ensure they held context for their own particular students. As an
example, teachers in Doone developed a question around investigating quadratics that was
KCTSequencing learning
trajectories
Developing contextualised questions
Analysing mathematical activities
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Lesson Study as a Model of in-school Professional Development
27
both mathematically relevant and would be of interest for their transition year group of male
students (Figure 9).
Figure 9 Contextualised question designed by teachers
Similarly in Crannóg teachers developed activities and tasks that incorporated learning
objectives with engaging problems. In their first research lesson teachers devised an inquiry
task introducing students to quadratic patterns (Figure 10).
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Lesson Study as a Model of in-school Professional Development
28
Figure 10 Contextualised student-inquiry activity
Analysingmathematicalactivities
Finally, teachers built on their KCT through analysing mathematics questions as a part of
their planning of research lessons. Through attempting these tasks with their colleagues,
teachers became aware of other solution strategies or aspects of questions that would
otherwise have been unfamiliar to them (Ball et al., 2008; Borko, Jacobs, Eiteljorg, &
Pittman, 2008). Furthermore, doing mathematics tasks prior to the research lesson
encouraged teachers to anticipate students’ mathematical responses, a feature of KCS.
In his second interview Dave reflected that in doing questions during the planning phase of
lesson study he had benefitted in terms of becoming aware of different approaches to
teaching that particular topic to students.
Dave I have looked at more ways of solving quadratics in the last week than I have looked at in the last ten years. I have tried more ways of solving quadratics in the last week than I have looked at in the last ten years. I had two methods, the method I used at school for ten years and the method I met with [my colleague] Fiona and I knew there were others out there. Now I am just reading different types with algebra tiles and with area models – considering more of the curriculum.
As with any professional development intervention, not all teachers gained in exactly similar
ways (Jacobs et al., 2010) but from analysis of the qualitative data the research suggests that
teachers built on their PCK through participation in iterative cycles of lesson study.
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Lesson Study as a Model of in-school Professional Development
29
ChangestoClassroomPractices
The most comprehensive change to classroom practice within research lessons was in
incorporating more student group work and more communication of mathematical thinking
through whole-class, pair, and group activities. In including these approaches to teaching
within research lessons, teachers observed the benefit of engaging students in problem
solving as a collaborative effort. The following is an excerpt from a post-lesson discussion
which demonstrated teachers’ surprise at the learning that occurred through students’
working in groups:
Walter It was more exciting for them than I thought it would be
Dave They came up with the questions themselves!
Walter Their imagination of it, they just sort of plugged into that more…
Fiona It worked. Those guys over there I was watching – they really helped each other. They were listening to each other!
Gerald All that dynamic is great, to watch how they are hitting off each other and when they have their own ideas. There was an excitement in there about getting stuff worked out.
Owen reported a dramatic change in his teaching from initially despising a “noisy classroom”
and considering himself as “anti Project Maths” to consciously incorporating whole class
discussions and including applications of mathematics within his teaching.
Following her conduction of the first research lesson, Lisa changed the layout of her
classroom from one based on individual student work to that of groups of students. When her
colleagues enquired about her changed classroom Lisa was extremely positive about how it
impacted on students’ learning which encouraged her colleagues to also incorporate student
group work in their classrooms.
Owen Are you happy with yours?
Kate You still have that layout?
Lisa Yeah! Because they can all see each other’s work ‘you’re not doing that right’. I don’t have to go as far as the group. I would never go back.
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Lesson Study as a Model of in-school Professional Development
30
Owen That’s great...Will I change the tables in my classroom for the day [of the research lesson] to have them in group work?
At the end of the year Lisa reflected that incorporating student communication of their
mathematical thinking within research lessons led to a dramatic change in how participating
teachers designed their classroom environment and activities.
Lisa I think we’ve all looked at the way our classrooms are set up – to facilitate cooperative learning. All of our classrooms were the traditional single look-at-the-board and everybody has used cooperative learning practices as a result of the lessons that we designed. Very little of our work was done for the kid to do on their own.
As well as these findings generated through a thematic analysis of the data, teachers also self-
reported changes to their classroom practices as a result of their participation in lesson study.
Both Walter and Eileen noted that from observing their colleagues, they were beginning to
consciously extend the ‘wait time’ in allowing students to answer during their own lessons.
Teachers were also consciously reducing their exposition time, instead incorporating more
opportunity for students to engage with mathematical activities within the lesson.
Furthermore, teachers in both schools were less dependent on textbooks to guide their
teaching. In Crannóg, teachers were already utilising textbooks as occasional question
sources and through lesson study, designed their own module on introducing calculus to
Transition Year students. In Doone, teachers became more and more proficient in designing
their own questions and realised that the textbook strategy did not always define a sequence
of learning that was relevant to their own students.
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Lesson Study as a Model of in-school Professional Development
31
In-School Professional Development
ComplementingIn‐serviceWorkshops
In both schools, teachers felt this form of professional development had particular benefit in
being located within the structures and cultures of their own schools where teachers
collaborated with their colleagues while focusing on their own students. Furthermore, where
teachers had attended professional development workshops outside of school and utilised
curriculum materials, they had not had opportunity to implement resources or ideas from such
in-service days. Lesson study provided teachers with opportunity to reflect on and
incorporate teaching approaches and resources which they had met in workshops and could
then modify and incorporate within their own teaching, relevant to their own students.
SchoolManagement
In both schools, the support of management was key in supporting teachers to participate in
this form of professional development and in this research (Fullan, 2003). Principals, vice-
principals, and other staff were supportive of their colleagues throughout the year and this
impacted positively on teacher learning and on the development of teacher community in
both schools. The support of principals and vice-principals in organising supervision for the
purposes of observation or planning was a positive influence on teachers’ engagement in this
form of in-school professional development.
VoluntaryProfessionalDevelopment
Although participation in professional development should include the majority of education
professionals and should occur regularly, participation in certain modules should occur on a
voluntary basis (Erickson, Minnes Brandes, Mitchell, & Mitchell, 2005). In this research, all
teachers reported in their final interviews that a vital element of their participation in this
research was that they had all volunteered in the intervention. Teachers felt it important that if
lesson study were to be incorporated as part of a suite of professional development models, it
should remain the choice of the individual teacher if they wished to participate.
In their discussions in both schools, teachers felt that they had benefitted from participating in
lesson study and wanted to continue with this form of professional development as a
mathematics teacher community. This was a possibility in Crannog where teachers requested
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Lesson Study as a Model of in-school Professional Development
32
a common free period in the following academic year but was not possible to continue in
Doone.
As a notable point, all teachers agreed that this form of professional development should be
included in additional contract hours as a form of structured teacher collaboration in subject
groups. A number of teachers expressed the wish for their participation in any professional
development to be officially recognised and felt that a lack of acknowledgement of their
engagement dis-incentivised teachers to continue with any form of professional development.
Scalability
While in this research there was not sufficient time to introduce teachers to lesson study prior
to their engagement in the model, the introduction of teachers to a model of lesson study
could be facilitated through research-based teacher education workshops mirroring Lewis et
al.’s (2009) research. Such workshops would incorporate teacher participation in activities
requiring facilitating of student group work and provide teachers with resources to share with
their colleagues. In introducing such a model to schools, teachers should be provided with
opportunity to volunteer to participate in the intervention which would necessarily adapt to
the structures and cultures within individual schools and mathematics departments. A small
number of well-trained facilitators would also be necessary as additional support for schools
engaging in initial cycles of lesson study.
SharingResources
In both schools teachers were happy to share the resources created in lesson study since they
were aware that their counterparts had given much of their free time in developing research
lessons. It is perhaps an important finding of this research that teachers were generous in
sharing the fruits of their collaboration with others who had proportionally invested time and
ideas into developing such materials.
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Lesson Study as a Model of in-school Professional Development
33
Limitations of the Research
In presenting this report it is necessary to recognise the limitations of the research.
One major limitation of this project is the sample population of the study. Only two schools
were involved in this research and while both phases of the curriculum reform were
represented, these two Mathematics departments cannot be stated as representative of all
Mathematics departments that may exist around the country. In addition, these schools were
both situated in Dublin and represented schools of large populations (over 500 students).
Further research may be necessary to investigate how smaller or more rural schools with
smaller populations of mathematics teachers might be impacted through participating in
iterative cycles of lesson study.
In referencing the scalability of this model of professional development and referencing
international research literature, I believe that lesson study can be introduced to post-primary
schools on both regional and national levels. Dudley (2012) along with many other
internationally based studies (C. Fernandez et al., 2003; Isoda & Katagiri, 2012; Murata et al.,
2012) have demonstrated the scalability of this model in schools all over the world.
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Lesson Study as a Model of in-school Professional Development
34
Conclusion
This research investigated lesson study as a model of school-based professional development
for Irish post-primary mathematics teachers and was conducted as a double case study based
in two schools. Lesson study was adopted as a model in order to structure the activities of
teacher community while providing teachers with opportunity to investigate their own
practices, through planning and reflection, at a time of curriculum reform.
Through planning multiple research lessons teachers collaborated in designing, conducting,
observing, and reflecting on mathematics lessons that were based within the Project Maths
initiative. Teachers became more aware of incorporating a critical student lens on their
practice in incorporating students’ prior knowledge, anticipating students’ mathematical
strategies, and interpreting students’ classroom responses. In engaging with the processes of
lesson study teachers became more comfortable in incorporating sociocultural practices
within their teaching by planning and reflecting on whole class discussions, in facilitating
student group work, and incorporating more communication of students’ mathematical
thinking. Furthermore, teachers designed their own mathematical activities and encouraged
students to engage in problem solving practices during research lessons. Through engaging in
iterative cycles of lesson study, all teachers of varying teaching experiences were facilitated
in developing their pedagogical content knowledge.
While these schools were both Dublin based, they represented schools of differing cultures
and ethos and provide evidence that lesson study may be introduced to Irish post-primary
schools as a voluntary form of teacher professional development. The support of school
management and teacher colleagues was incredibly important in promoting their colleagues’
engagement with this research for the course of the academic year.
Lesson study, while seemingly simple to describe, holds much power in how it can engage
teachers in investigating their own practices and in providing an environment within which
mathematics teachers can be creative in their teaching. It also provides teachers with unique
opportunities to access how students respond to and engage within mathematics lessons and,
as identified in this research, participation in iterative cycles of lesson study can build
teachers’ pedagogical content knowledge.
This is a model of professional development which holds great potential as a structure within
which teachers can enjoy, learn from, and reflect on their practices of teaching mathematics.
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Lesson Study as a Model of in-school Professional Development
35
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Appendices
Appendix A: The Lesson Study Cycle
1. Study Curriculum and Formulate Goals
During the first meeting of the community of practice the following agenda is suggested:
A. Choose roles for the initial meeting: time keeper, note taker, facilitator etc.
B. Examine everyone’s ideas about professional development and lesson study
C. Consider long-term goals and/or lesson goals
D. Build a timeline for the lesson study cycle
E. Review the curriculum and areas or topics which may be of interest
F. Review key decisions and/or insights made during the meeting
G. Agree upon assignments to be completed or followed up in the next meeting.
Facilitator: The facilitator’s role is to aim to ensure that the preceding steps are met during
the meeting or will agree with the group that they will be addressed at the next meeting. It is
important that while an agenda is adhered to, the facilitator’s role should be fluid and allow
conversations to run freely.
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Lesson Study as a Model of in-school Professional Development
40
Long term goals
In considering long-term goals teachers may ask themselves:
What is a gap between the ideal and the actual that you would really like to work on as a teacher?
Think about the students you serve. What qualities would you like these students to have in 5 or 10 years from now?
What qualities do they have now and what could be improved upon?
Teachers should agree on the phrasing and terminology of their long term goal particular to
their own set of students. This goal should remain a focus for all of the lesson study cycles
throughout the year.
Examples:
For our students to find purpose in their mathematics and meaning that leads to their
enjoyment and confidence in the subject.
Creating a culture which fosters independent thinking and fearlessness leading to
autonomous learners.
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Lesson Study as a Model of in-school Professional Development
41
2. Planning a Research Lesson
Planning Meetings
A. Choose roles for the planning meeting: note takers, lesson plan recorder, time keeper,
facilitator, etc.
B. Decide on the class group and curriculum area on which to focus.
C. Select the lesson you will focus on.
D. Write a teaching and learning plan over a number of meetings (You may wish to use
and/or modify resources already available to you).
E. Devise an observation strategy for collecting data.
F. Review key decisions and/or insights made during the meeting.
G. Agree upon assignments to be completed or followed up in the next meeting.
Teaching and Learning Plan
The teaching and learning plan should include:
Long term goals
Anticipated student thinking
Data collection plan
A sequence of learning
The rationale for this chosen approach
In creating the teaching and learning plan teachers may wish to ask themselves:
(Note: These questions are only a guide)
1. What do students currently understand about this topic?
2. What do we want them to understand at the end of the unit or sequence of lessons?
3. What’s the sequence of experiences (lessons) that will propel students toward the
learning objective?
4. What will make the unit/sequence of lessons and each individual lesson motivating and
meaningful to students?
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5. Which lesson in the unit will be selected as the research lesson?
6. What will students need to know before this lesson?
7. What will they learn during this lesson?
8. What is the sequence of experience through which they will learn it?
9. How will students respond to the questions and activities in the lesson?
10. What problems and misconceptions will arise and how will teachers respond to them?
11. What evidence should we gather and discuss about student learning, motivation, and
behavior?
12. What data collection forms are needed to do this?
Each member of the planning team should independently do the activity intended for students
within the research lesson. Usually in a group of teachers, there will be a variety of strategies
in attempting an activity and each teacher should have an opportunity to share how they
approached the activity. It will be important to discuss the successes and difficulties the
students will encounter and also the successful process(es) and outcomes for this task.
The point of anticipating student responses is not to design the activity so that student’s won’t
struggle or so that misconceptions won’t emerge, but rather to give teachers an opportunity to
plan how they will respond and to think about what kind of struggles and misconceptions
may be an intentional element of the lesson. It is important to discuss the instructional
strategies and options that might facilitate the student learning as struggles and
misconceptions emerge. Record the anticipated student responses and teacher responses in
the lesson plan.
Approximate
Time Guide
Student
Learning
Activities
Anticipated
Student
Responses
Anticipated
Teacher
Responses
Points to notice
& evaluate
Figure 11 Suggested headings for a Teaching & Learning plan
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Collecting Data
It will also be important for teachers to reflect on what data collected during the lesson will
assess the learning and engagement of students.
NB: It may be useful for observing teachers to have both a copy of the lesson plan and
seating map of the room with students’ names during the lesson.
________________________________________________________________
In designing and observation sheet teachers should ask:
1. What data will help you understand your students’ progress on your lesson
goals and long-term goals?
2. Would a prepared data collection form facilitate observation or should
conversations between students be recorded?
3. What student work (if any) will be collected at the end of the lesson?
4. How will material that is presented on the board or in other locations be
captured? (Photographs etc.)
5. What are the individual assignments of the lesson study team? Will one person
transcribe the lesson and keep a timeline of lesson events? Will observers be assigned to
observe specific students or groups?
6. If the lesson is to be video-recorded, who will be in charge of the video
equipment during the lesson?
________________________________________________________________
It is not necessary to write an answer for every question but it is important to discuss the
questions within the meeting. You may wish to write your Lesson Plan as a mind map but it
is important that there is a written record for you and your colleagues to return to for the
reflection and following the Lesson Study cycle.
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3. Conducting and Observing the Research Lesson
Teaching the Lesson
The teacher who will be instructing the lesson should follow the Teaching & Learning plan or
may construct a condensed Lesson Flow for themselves. The teacher may introduce the class
to the observing teachers but otherwise should not interact with his/her colleagues during the
lesson. This teacher is conducting the lesson that all members of the group have designed.
Recommendations for observing teachers
Minimise side conversations during the lesson
Remain in the classroom during the entire lesson to capture how the lesson is set up, its flow,
and its conclusion
Do not block the students’ view of the blackboard or any area where the teacher is
writing and posting materials or demonstrating an activity
Minimise interactions with students. Refrain from teaching or assisting the students.
Occasional interaction is permissible if done discreetly and with the purpose of
understanding student thinking.
Observing teachers should choose specific behaviours or actions to focus on during the
lessons. Teachers may wish to address specific research questions during the lesson and/or
use observation forms.
Note: The observing teachers are explicitly focusing on students’ engagement and learning
during the lesson and not on their colleague’s teaching.
________________________________________________________________
Suggested Observations to Note
• Comments that come to your mind as you observe. • Critical things that are happening in the classroom. • Types of questions the students ask. • Types of questions the teacher asks. • Evidence of higher-order thinking. • Evidence of confusion. • Number of times students refer to and build on classmates’ comments. • Evidence of engagement.
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4. Reflect on the Research Lesson
Reflection Meeting
A. Choose roles for the planning meeting: time keeper, note taker, facilitator etc.
B. The lesson teacher should first share their reflections on the lesson.
C. Observing teachers should share data and reflections from the lesson (each person
should have an opportunity to share their opinions and provide evidence for their
observations).
D. Use the data to highlight student learning, lesson design, and any broader issues in the
teaching & learning.
E. Reflect on any changes that should/not be made to the Teaching & Learning template
and decide whether or not to teach this adjusted plan or embark on a new cycle.
F. Record any changes to the Lesson Study plan and make note of new ideas that have
resulted from the observation of the lesson.
G. Review key decisions and/or insights made during the lesson study meeting.
H. Agree upon assignments to be completed or followed up in the next meeting.
Note: If the group agrees to revise and re-teach the lesson, what changes affected the student
learning? How was the learning affected?
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Appendix B: Materials for use during lesson study
Long-term Goals and Objectives
Personal Objectives
Teaching Objectives
Classroom Objectives
Objectives for Students
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Teaching-Learning Plan
Participating Teachers
Instructor
Date
Intended Class & Year Group
Lesson Title
Research Theme/ Subject Matter Goals/ Lesson Goals
Lesson Rationale
Why focus on this topic? What is difficult about learning or
teaching this topic? What is currently noticed about students
learning this topic? Why we have designe